Recently, Ben Green proved that the two-color van der Waerden number ω(3, k) is bounded from below by $${k^{{b_0}\left( k \right)}}$$ where $${b_0}\left( \right) = {c_0}{\left( {{{\log \,k} \over {\log \log \,k}}} \right)^{1/3}}$$ . We prove a new lower bound of kb(k) with $$b\left( {{c\log \,k}}$$ This done modifying Green’s argument, replacing complicated result about random quadratic forms a...

‎In this paper we consider the special classes of Sonnenschein matrices‎, ‎namely the Karamata matrices $K[alpha,beta]=left(a_{n,k}right)$ with the entries‎ ‎[{a_{n,k}} = sumlimits_{v = 0}^k {left( begin{array}{l}‎ ‎n\‎ ‎v‎ ‎end{array} right){{left( {1‎ - ‎alpha‎ - ‎beta } right)}^v}{alpha ^{n‎ - ‎v}}left( begin{array}{l}‎ ‎n‎ + ‎k‎ - ‎v‎ - ‎1\‎ ‎,,,,,,,,,,k...

in this paper, we firstly show that the $n$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $n$-dual operation. as a dual result, the $n$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

background: diagnosis of kidney scar could prevent vesico urethral reflax and its complications such as hypertension and renal failure. this study was conducted to determine average kidney length and volume in infants by sonography to accurate diagnosis of scars. methods: this study was conducted on infants with the history of uti who referred to imam reza hospital, kermanshah iran, for dmsa sc...

Let G n $$ {G}_n be a random geometric graph, and then for q , p ∈ [ 0 1 ) q,p\in \left[0,1\right) we construct ( \left(q,p\right) -perturbed noisy graph {G}_n^{q,p} where each existing edge in is removed with probability while non-existent inserted . We give asymptotically tight bounds on the clique number ω \omega \left({G}_n^{q,p}\right) several regimes of parameter.